Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.9815)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=-5/2, a₂>=-5/2

For fixed z and a₁=-5/2, a₂=3, b₁>=-11/2

For fixed z and a₁=-5/2, a₂=3, b₁=-9/2

http://functions.wolfram.com/07.25.03.9815.01

Input Form

HypergeometricPFQ[{-(5/2), 3}, {-(9/2), -(9/2)}, z] == (1/59535) (59535 - 22050 z + 5400 z^2 - 720 z^3 - 240 z^4 - 2016 z^5 - 14400 z^6 - 8960 z^7 - 1440 z^8 - 64 z^9) - (16 E^z Sqrt[Pi] (390 z^(11/2) + 1140 z^(13/2) + 603 z^(15/2) + 92 z^(17/2) + 4 z^(19/2)) Erf[Sqrt[z]])/59535

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]